Abstract

Processes that use mechanical positioning of reactive species
to control chemical reactions by either providing activation energy or
selecting between alternative reaction pathways will allow us to construct
a wide range of complex molecular structures. An example of such a process
is the abstraction of hydrogen from diamond surfaces by a radical species
attached to a mechanical positioning device for synthesis of atomically
precise diamond-like structures. In the design of a nanoscale, site-specific
hydrogen abstraction tool, we suggest the use of an alkynyl radical tip.
Using ab initio quantum-chemistry techniques including electron
correlation we model the abstraction of hydrogen from dihydrogen, methane,
acetylene, benzene and isobutane by the acetylene radical. Of these systems,
isobutane serves as a good model of the diamond (111) surface. By conservative
estimates, the abstraction barrier is small
(less than 7.7 kcal mol-1)
in all cases except for acetylene and zero in the case of isobutane.
Thermal vibrations at room temperature should be sufficient to supply the
small activation energy. Several methods of creating the radical in a controlled
vacuum setting should be feasible. Thermal, mechanical, optical and chemical
energy sources could all be used either to activate a precursor, which
could be used once and thrown away, or alternatively to remove the hydrogen
from the tip, thus refreshing the abstraction tool for a second use. We
show how nanofabrication processes can be accurately and inexpensively
designed in a computational framework.

1. Introduction

Mechanical positioning of reactive species can be used to convert mechanical
energy to chemical energy to select between alternative reactions, or to
provide activation energy. Mechanosynthesis is the employment of these
mechanochemical processes to synthesize molecular structures [1]. Atomically
precise mechanosynthesis promises to let us manufacture complex systems
of molecular machinery. Examples include: self-replicating assemblers [2],
molecular-scale surgical systems [2], computers made with molecular logic
elements [3] and macroscopic machines made of diamond-like materials. Construction
of such systems will require the ability to manipulate structure precisely
on an atomic level. The great specificity of the chemical reactions required
to synthesize designs with specific atomic structures should be achievable
with mechanochemical tools capable of positioning the reactive moieties
with sub-angstrom accuracy. Mechanochemistry allows alternative reaction
transition states to be selected by manoeuvring the reactive species into
a position where the chosen reaction has the smallest barriers. Such positional
control requires that the tool exert forces and torques on the reactive
molecule to move it over the potential energy surface of interaction with
the workpiece.

Applying positional control to reactions will require that the tool
have certain properties to make synthesis reliable, feasible and practicable.
The tool must (i) have the proper chemical properties, (ii) be relatively
small to reduce steric interactions with the workpiece, (iii) be capable
of remaining chemically and mechanically stable under thermal motions and
strains induced during positioning, (iv) be bound to a system that can
transfer forces and torques to the reactive portion of the tool, (v) be
selective between alternative reactions and (vi) be easily made. Molecular
tips attached to atomic force microscope (AFM) tips, scanning tunnelling
microscope (STM) tips or molecular robotic arms have been suggested [4].

Because construction of atomically precise machinery might require about
as many unit operations as there are atoms in the system, it is important
that reactions be fast. To increase the speed of reactions with moderate
barriers, forces can be exerted between the workpiece and reactive species
to effectively increase the pressure on the system, reducing the barrier
height. Moderate reductions in the barrier heights lead to substantial
increases in the reaction rate because thermal vibrations have an
exponential Boltzmann probability of overcoming the reaction barrier.
Mechanochemistry
not only reduces the barriers by converting mechanical energy to chemical
energy, but also maximizes the effective reactive concentration by positioning
the reactive moieties to best advantage. These speed-enhancing steps together
with having many mechanochemical machines working
simultaneously can compensate
for the loss of parallelism of solution-based reactions. Mechanochemical
synthesis also increases the range of synthetic steps that can be used
to build novel structures by the use of applied torques; a moiety attached
to both the tool and the workpiece can be twisted, for example, to break
pi-bonds [1].

Nanomachines made of complex specific arrangements of diamond-like
material offer several advantages.
First, diamond is light and stiff. Macroscopic
machines could be made stronger and simultaneously much lighter, making
such activities as air and space travel substantially more practicable.
Moving parts of such machines would be lighter and therefore faster.
Furthermore,
hydrocarbons are abundant, making raw materials readily available
and inexpensive. Stiffness is not only a desirable property of finished
machines, but it is also useful during construction since the material
surrounding the reactive site on the workpiece must be stiff. This allows
it to withstand the compressive forces that might be needed to reduce reaction
barriers, to withstand the tensile forces during moiety abstraction and
to withstand torques applied to break pi-bonds.

Building machines of diamond will include manoeuvring hydrocarbons
into reactive sites, torsion of structures,
insertions into bonds and preparation
of reactive sites by removing unwanted moieties to create radical sites.
Abstraction of hydrogen is likely to be the most repeated step and common
to building a wide range of molecular structures, including diamond-like
structures. Highly reactive species are commonly thought to play a crucial
role in the chemical vapour deposition (CVD) synthesis of diamond [5-7].
The abstraction of hydrogen via any of several radicals is one of the central
mechanisms involved in the growth of diamond.
It is not unreasonable, therefore,
to expect that the atomically precise synthesis of diamond-like materials
will utilize site-specific hydrogen abstraction via a radical as one of
the main steps.
Drexler has proposed using a molecular
tip made of an ethynyl radical [1]

While many radicals
exist, the desire for a simple,
general, positionally accurate and sterically undemanding hydrogen
abstraction tool can be used to narrow the search to a structure that (i)
has a very high affinity for hydrogen, (ii) is not encumbered by surrounding
groups,
(iii) can be made part of an extended structure, which can be used
as a 'handle' for positioning and can be attached to an STM or AFM tip,
(iv) is mechanically and chemically stable during positioning, (v) is selective
between alternative reactions such as abstraction of a neighbouring hydrogen
or bonding to a nearby carbon atom and (vi) is easily made or regenerated.
Perhaps the most natural structure in this regard is the ethynyl radical.

The C-H bond in acetylene is one of the strongest bonds to hydrogen;
thus, the ethynyl radical formed by removing this hydrogen is likely to
have a higher affinity for hydrogen than almost any other chemical structure.
Further, the ethynyl radical can easily be incorporated into structures
that provide a high degree of steric exposure. A structure resembling the
propynyl radical, but with the carbon furthest from the radical site embed
ded in an extended diamond-like structure (figure 1), provides both excellent
steric exposure to the radical and a 'handle' for positioning the radical
for the desired abstraction. Attachment of the tool to an STM or AFM tip
may develop from technology designed for attachment of proteins to surfaces
[4]. Drexler showed that the bending stiffness of an ethynyl-like tip attached
to an adamantyl group is 6 N m-1
and can be increased to ~65 N m-1
by building up a surrounding collar [1]. If the reaction
requires application of mechanical force to supplement
thermal energy, then bending stiffness may need to be
increased. Stiffness also is desirable to achieve selectivity.
STM and AFM positioning is stable to more than
sub-angstrom accuracy. However, bending modes of the
ethynyl tip will be active at moderate temperatures. If
during positioning of the tip, the bending of the radical
and displacement of the AFM or STM relative to the
work piece positions the reactive portion of the tip near a
branched transition state, for example (one pathway
leading to abstracting the neighbouring hydrogen), then
selectivity is reduced. Drexler has shown that at worst at
room temperature with a bending stiffness of 20 N m-1
and transition states separated by 1.2 Å the unwanted
reaction rate is less than 10-12 times the
rate of the target
reaction [1]. Transition states between neighbouring
hydrogens on the (111) surface of diamond are separated
by 2.5 Å, and transition states for other possible reactions
in diamond-like structures also generally exceed 1.2 Å,
making mechanochemical reactions highly selective.

Table 1. Experimental bond dissociation energies
(kcal mol-1).

R-H

D0

H-H

102.3 [25]

CH3-H

105.1 [27]

(CH3)3C-H

93.2 [27]

C6H5-H

110.9 [27]

HCC-H

126.6 [11], 131.3 [9]

The strong C-H bond of alkynes
(127-132 kcal mol-1 [8-12] should give large
exothermicities
and small barriers (rapid reactions) for alkynyl radical
abstraction of hydrogen from weaker sp2 and
sp3 hybridized C-H bonds (see table 1).
The large exothermicity
would also give a small reverse reaction rate constant. Compressive
mechanical forces could be applied to supplement thermal energy in cases
where the barriers are large; however, care must be taken so that the alkynyl
radical tip does not bend away from the transition state. In the cases
we study the barriers are such that this is not an issue.

Several methods of creating the radical should be feasible. The
process of creating the radical should take place in an inert environment:
vacuum, helium, or some other extremely non-reactive system would be
appropriate.
The activation energy required to create the abstraction tool could
be provided from thermal, mechanical, optical, or chemical sources. There
are two obvious approaches. In the first, a precursor compound is activated
to create the abstraction tool. The tool is then used once and discarded.
A second precursor would then be activated to abstract a second hydrogen.
Thus, in a functioning system using this approach, a steady supply of the
precursor would be required as well as a method for disposing of the 'used'
abstraction tools.

In the second approach, the abstraction tool would be refreshed
by the removal of the hydrogen after each use. Of course, the ethynyl radical
was selected on the basis of its strong C-H bond, so removal of the hydrogen
might at first seem paradoxical. However, there are several methods of
solving this problem. One would be first to weaken the C-H bond, and then
abstract the hydrogen from the abstraction tool using a weaker radical.
Drexler [1] proposed that the C-H bond could be weakened by positioning
a weak radical near the carbon atom. A second weak radical could then abstract
the hydrogen from the tip.

An alternative to the 'attack by two weak radicals' strategy would
be photoexciting the acetylene to obtain the pi pi* state,
which would rearrange
to the structure

with a weak C-H bond and thereby allow removal of the hydrogen.
Our primary concern is to analyse the energy barriers associated with hydrogen
abstraction using alkynyl radicals to determine the feasibility of such
a tool, rather than to analyse the methods of creating such a tool.

We model the chemically active site of the tool by the acetylene
radical and determine the transition-state geometry and activation energy
for transferring the hydrogen from several species:
H2, CH4, C2H2,
C6H6
and CH(CH3)3.
The geometry of the various transition states can be used
to position a working hydrogen abstraction tool for fast reaction and so
as not to bend the tip. The barrier height itself can be used to calculate
an abstraction rate at a given temperature and, thus, how long the abstraction
tool must remain at the transition state until the probability that abstraction
has occurred reaches a given value. Various levels of generalized valence-bond
(GVB) and configuration-interaction (CI) ab initio calculations
are used. To calibrate the accuracy of these calculations, we consider
the abstraction barriers and transition states for hydrogen transfer between
methyl and methane and for hydrogen transfer between H and
H2 as compared
to other theoretical and experimental results [13-15].

Figure 2. Schematic diagram showing the transition barrier and exothermicity
of the acetylene radical abstraction of hydrogen from isobutane.

a:
In the case of H-H-H, the CCCI, DCCI and GVB.SDCI (three reference
SDCI) are equivalent calculations.

b: Negative values indicate that the CCCI
transition-state geometry is lower in energy than the reactants at this
level of calculation. This suggests that no barrier exists on the potential
energy surface.

c: Numbers
in parentheses are the barriers when the Davidson correction
is included.

The barrier to the acetylene radical abstraction of hydrogen from
isobutane (sp3 carbon) is
conservatively estimated to be less than 0.45
kcal mol-1 (figure 2).
Reaction barriers calculated at various levels of
correlation are shown in table 2. The barrier to abstraction of hydrogen
by the acetylene radical from benzene (sp2 carbon)
is estimated to be less
than 7.7 kcal mol-1.
The Hartree-Fock times singles and doubles configuration
interaction (HF*SD CI) consistently overestimates the generalized valence
bond times singles and doubles configuration interaction (GVB*SD CI)
barriers, while the
dissociation-consistent configuration interaction (DCCI) consistently
underestimates the GVB*SD CI barriers. The GVB*SD CI barriers will be
conservatively high due to a lack of a third diffuse p function, zero-point
corrections and lack of more correlation of the valence electrons. Transition
states were optimized at the correlation-consistent configuration interaction
(CCCI) level (table 3). Although CCCI does not accurately predict activation
barriers, it does accurately describe the transition-state geometries.
For the largest cases,
the number of spin eigenfunctions in the configuration-interaction
(CI) calculation grows beyond our computational capabilities (table 4).
This makes abstraction from benzene and isobutane at the GVB*SD CI level
impracticable; however,
the overestimated, yet small, barriers at the HF*SD CI level show that
the acetylene radical hydrogen abstraction is feasible, thermal vibrations
at room temperature providing sufficient energy to overcome the barriers.
Table 5 shows the exothermicities for the various abstractions. There is
little difference in the accuracy of the methods
in predicting the exothermicities
because all the methods describe bound states rather well. Note that the
exothermicities are for reactions where the product radical species are
not allowed to relax. This describes abstraction from surfaces where relaxation
is constrained. Exothermicities for gas-phase reactions will be higher.
The transition state is poorly described by many semi-empirical methods
and by ab initio methods with
insufficient electron correlation and small basis sets, and large variation
of the predicted barriers can be seen in table 2.

Table 3. Transition-state geometries optimized at the CCCI level. See
text for constraints on these geometries.

R1-H-R2

R1H bond length (Å)

R2H bond length (Å)

H-C-H anglea (deg)

H-H-H

0.94

0.94

CH3-H-CH3

1.36

1.36

105.2

H-H-CC-H

0.80

1.61

CH3-H-CCH

1.22

1.48

105.5

(CH3)3C-H-CCH

1.2

1.5

C6H5-H-CCH

1.24

1.42

HCC-H-CCH

1.28

1.28

&nbsp

a: This is the angle between the methyl hydrogens and the C-H-C axis.

Table 4. Number of spin eigenfunctions in each of the Cl calculations.
The numbers in parentheses are the number of spin eigenfunctions for the
separated cases, R1-H + R2, where symmetry is broken.

R1-H-R2

CCCI

DCCI

HF*SD CI

GVB*SD CI

H-H-H

191(386)

191(386)

139(278)

191(386)

CH3-H-CH3

4914(9829)

71666(143333)

79428(158757)

310778(621164)

H-H-CCH

2160

18234

15189

53048

CH3-H-CCH

9477

150557

184851

737651

(CH3)3C-H-CCH

21676

695842

1675566

C6H5-H-CCH

17265

587343

1514151

HCC-H-CCH

2697(5398)

42201(84406)

55211(110314)

221805(443182)

Table 5. Calculated
exothermicities (kcal mol-1).

R1-H-R2

HF

GVBCI-SCF

CCCI

DCCI

HF*SD CI

GVB*SD CI

H-H-CCH

33.9

31.6

31.8

30.1

30.0(27.5)a

29.9(28.1)

CH3-H-CCH

28.9

28.4

27.0

29.2

26.9(25.5)

26.8(25.4)

(CH3)3C-H-CCH

28.5

27.9

24.2

27.4

26.8(25.9)

C6H5-H-CCH

18.7

18.2

15.4

18.9

18.3(18.0)

a: Numbers in parentheses include the Davidson correction.

3. Calculational details

Standard ab initio quantum-chemistry methods are
employed and results are given for several levels of calculation. The
simplest wavefunction used is the wavefunction in which each molecular
orbital is doubly occupied. This single-configuration (one-determinant)
Hartree-Fock (HF) wavefunction is the lowest-energy antisymmetrized
n-fold product of molecular orbitals and should give a qualitative picture
of the hydrogen abstraction reactions studied.
HF will tend to overestimate
the abstraction barrier since the radical-hydrogen stretching frequency
is too high due to the poor description by HF of the bond breaking
process (a doubly occupied orbital of the molecule must become two singly
occupied orbitals for the fragments). This problem is remedied by using
a GVB (generalized valence-bond) wavefunction [16], which allows each bond
to be described with two singly occupied, overlapping orbitals leading
to a proper description of dissociation. When solved for self-consistently,
this calculation is termed a generalized valence-bond configuration-interaction
self-consistent field (GVBCI-SCF) or equivalently a complete active space
self-consistent field (CASSCF). Simply, all symmetry- and spin-allowed
configurations of three active electrons in three orbitals are generated.
These electrons are the radical of the reactant, the hydrogen and the radical
of the product. All other orbitals (considered inactive) are doubly occupied
as in Hartree-Fock. It is found that three configurations are all that
is necessary to describe the transition state adequately. These are the
dominant configuration (with the Hartree-Fock occupations of the orbitals)
and the single and double excitations of the electrons in the doubly occupied
R1-H-R2 bonding orbital to the empty
R1-H-R2 antibonding orbital. The
R1-R2 antibonding orbital
(with a node at the hydrogen centre) is singly
occupied in all three configurations. While this level of calculation includes
the most important correlation, it will still tend to overestimate the
abstraction barrier and, thus, will only serve as a zeroth-order wavefunction
for large CI (configuration-interaction) expansions, which will account
for additional dispersion.

Ideally, we would like to do a CI calculation in which
all single and double excitations of the valence electrons are made
into the virtual orbitals with reference to
the three most important configurations
describing the abstraction. This type of multi-reference CI (called a
GVB*SD CI) has been well established in approximating results of complete
CI calculations [17]. However, this CI has not been carried out for the
largest cases, abstraction of hydrogen from isobutane and benzene by the
acetylene radical. Thus we have considered some smaller CI calculations,
which will do a good job in approximating the barriers for the larger CI.
The first of these is the CCCI wavefunction [18, 19]. It involves making
all single and double excitations of the active electrons and all single
excitations of the other valence electrons into the virtual space relative
to the three GVB references, or simply GVB*(SDactive
+ Svalence). The
second CI, called a DCCI (dissociation-consistent configuration interaction),
will add the double excitations, which are the product of a single excitation
of an active electron and a single excitation of a valence electron, or
GVB*(SDactive + Sactive*Svalence
+ Svalence). The third
CI does all single and double excitations of the valence electrons (active
and inactive) relative to only one reference, a calculation called
HF*SD CI
(or equivalently one-reference SDCI). Table 4 shows the sizes of
the CI expansions in terms of the number of spin eigenfunctions (SEF) for
each of the systems studied. The HF*SD CI already approaches the limits
of our programs (about two million SEF) in the cases of isobutane and benzene,
for which the GVB*SD CI is not possible. In all other cases, however,
the GVB*SD CI are of small to medium size and will serve as benchmarks
to calibrate the accuracy of the smaller CI.

The standard basis sets of Dunning and Huzinaga are used [20,21]. Their
double-zeta contraction of the 9s5p set is used on all carbons, with the
addition of one set of d polarization functions (Zd
= 0.75). On
the active carbons, diffuse s and p functions (Zs
= 0.0474 and Zp = 0.0365)
are also added. For active hydrogens or hydrogens bound to active carbons
(in the case of methane), the triple-zeta contraction of the 6s set is
used, supplemented with a p polarization function (Zp
= 0.60).
For all other hydrogens, the double-zeta contraction of the 4s set is
used, scaled by a factor of 1.2.

Figure 3. Geometries
for the transition states.

The basic geometries of the various systems studied are illustrated
schematically in figure 3. The geometries will be optimized at the CCCI
level. The orbital optimization
at the GVBCI-SCF level is the most time-consuming
step, so this CI will be a simple correction to that wavefunction. It would
be impracticable to do the
geometry optimization at a higher-level CI. It would also be impracticable
to do a full geometry optimization, so certain constraints are assumed.
Namely, only the parameters relevant to the description of the hydrogen
abstraction (R1H and R2H or combinations thereof)
will be optimized. In
the case of abstraction from methane (by the methyl radical or by the acetylene
radical), the H-C-Habs bond angle is also
optimized since this angle changes
from 109.5° for methane to 90° for the methyl radical.
For isobutane, we
would expect a small relaxation from a tetrahedral
C-C-Habs bond angle
to something more planar at the transition state and in the radical species.
But Page and Brenner [22], in their work on abstraction of hydrogen from
isobutane by atomic hydrogen,
found that full relaxation of the t-butyl
species reduced the abstraction barrier by only 1.7
kcal mol-1 at the GVBCVI-SCF level.
GVBCI-SCF level.
However, since the goal of this work is to show the feasibility
of using an alkynyl radical tip as a hydrogen abstraction tool, a conservative
overestimate of the abstraction barriers is acceptable.
So the C-C-Habs
bond angle is fixed to 109.5° in these calculations.
All other radicals
are expected to show little or no relaxation and are fixed to the experimental
values of their hydrogen bound counterparts.

All calculations are run with the GVB [23] and MOLECULE-SWEDEN
(an electronic structure
program system written by Almlof et al [24]) suites of programs
on the Caltech group's Alliant FX/80 and FPS5OO.

4. Discussion

4.1. H-H-H

A great deal of theoretical work has been done
on this system [15]
and, owing to its simplicity, it provides a good test of our hydrogen
basis set and, to a lesser extent, our methods.
While the calculated equilibrium
bond distance in H2
compares favourably with experiment (0.74 Å
vs. 0.74144 Å [25]), the calculated dissociation energy for
H2 (De) is
105.4 kcal mol-1 compared with the experimental
108.6 kcal mol-1 [25].
This discrepancy of 3 kcal mol-1
is chiefly due to the lack of a second
p polarization function. In contrast,
the transition state is well described
by the GVB*SD CI (in this case only, the CCCI,
DCCI and GVB*SD CI
are equivalent since there are no valence electrons in addition to
the three active electrons). The optimized geometry has a H-H distance
of 0.94 Å (compared to Liu's value of 0.930 Å [15])
and a barrier
of 10.3 kcal mol-1
(compared to Bauschlicher's value of 9.56 kcal mol-1
using a large atomic natural orbital (ANO) basis set [15]). The
geometries for all the systems studied are listed in table 3
and the abstraction
barriers are listed in table 2. An error of less than 1 kcal in the barrier
is adequate for the calculations at hand, particularly since the barrier
is overestimated. It should be noted, however, that the Hartree-Fock barrier
is well off the mark at 24.3 kcal mol-1
and that the apparently good result
at the GVBCI-SCF level (9.9 kcal mol-1) is primarily due
to the weak H-H bond strength (87.5 kcal mol-1)
at this level. The HF*SD CI
number including the Davidson correction is in fortuitous agreement
with the reference barrier height of 9.56 kcal mol-1.
This is rather symptomatic
of the Davidson correction, which can often overestimate the contributions
from additional correlation.

4.2. CH3-H-CH3

The methyl-methane hydrogen transfer reaction is perhaps
more representative
as a test case of the systems in which we are most interested. There has
been less theoretical work done on this system [14] but a reliable experimental
number for the abstraction barrier of 14.2 kcal mol-1
[13] gives a good
benchmark for us to work with. Theoretical investigations into this reaction
have not been successful in obtaining quantitative accuracy in the barrier
height. The best calculations overestimate the barrier by
5-6 kcal mol-1. Part
of this is due to some assumptions made in the calculations, namely the
neglect of zero-point corrections, the Born-Oppenheimer approximation
and temperature effects.
However, the sum of these effects should only lower the theoretical
activation energy by 1-2 kcal mol-1(see Sana et
al [14]). Our results agree well with previous
theoretical work. The optimized transition-state geometry is virtually
identical to the full gradient optimized structure of Wunsch et
al [14], which was done at the Hartree-Fock level. The calculated barrier
is 20.4 kcal mol-1, higher than experiment by
6.2 kcal mol-1. Test calculations with a large ANO basis set
[26] only lowered the barrier to 19.2 kcal mol-1, indicating
that the discrepancy between theory and experiment is probably a correlation
problem rather than a basis set problem. The importance of ionic terms
such as (CH3-H+--CH3)
are probably underestimated in the CI calculations
owing to biases against anionic states and would require additional
correlation of the non-active valence electrons. This could be a
formidable task even for such a small system and would not be possible
with our current code for the larger cases we wish to study. However,
again, since these factors all tend to lead to an overestimate of
the barrier height, the results for abstraction of hydrogen by the acetylene
radical can be considered a conservative upper limit to the actual barrier
height. These calculations on the methyl- methane system also offer
a comparison of the smaller CI to the GVB*SD standard.
We find the CCCI result (29.8 kcal mol-1) to
be comparable to the GVBCI-SCF number (27.8 kcal mol-1),
being slightly higher due to the stronger C-H bond
at the CCCI level (113.2 kcal mol-1
vs. 97.6 kcal mol-1 at
the GVBCI-SCF level and 107.2 kcal mol-1 at the GVB*SD
CI level). This indicates that correlation of the non-active electrons
is important in obtaining quantitative accuracy for the
hydrogen abstraction
barriers. The DCCI, which includes only limited correlation of the
inactive electrons, underestimates the GVB*SD CI barrier by
2.9 kcal mol-1.
Alternatively, the HF*SD CI, which sacrifices some of the active
electron correlation, overestimates this barrier by 2.1
kcal mol-1. The
combination of these two CI calculations should offer an upper and
lower limit to the GVB*SDCI for those large cases where that CI is
not feasible.

4.3. H-H-CCH, CH3-H-CCH,
C6HH-CCH and HCC-H-CCH

Results of calculations on these systems underscore the results
of methyl-methane. In particular, Hartree-Fock greatly overestimates
the activation energies, GVBCI-SCF and CCCI
offer some improvement
but still overestimate these barriers, and DCCI and HF*SD CI bracket
the results of the GVB*SD CI. In the case of abstraction from methane and
benzene, we found that the geometries were most conveniently optimized
by using the coordinate system R1H +
R2H and R1H - R2H.
In the case of abstraction from H2,
it was easier to optimize the transition
state in terms of the coordinates R1H and R2H.
This was probably due
to the fact that the barrier was small at the CCCI level and that
it occurred quite early, with only an 8% increase in the H-H bond length.
To a large degree the barrier height and the position of the barrier are
determined by the exothermicity of the reaction. Other properties, such
as the polarizability of the bonds, play a role as well. The
largest barrier (and latest transition state) was for abstraction
from acetylene, with an activation energy of 14.6 kcal mol-1. This
is as expected, since this particular reaction is thermoneutral. The calculated
exothermicities of the other reactions are listed in table 5 (see
also table 1, for the experimental bond dissociation energies).
H2 and
CH4 are the most exothermic and have the smallest barriers.
These barriers
may be considered negligible as the calculations on
H + H2 and methyl-methane
showed the numbers to be overestimated. Abstraction from benzene is less
exothermic and shows a small but non-negligible barrier. In addition the
phenyl-H bond is stretched 14% at the transition state in comparison to
an 11% stretch of the methyl-H bond. All of these results correlate with
the exothermicities of the reactions.

4.4. (CH3)3C-H-CCH

Finding the transition state for abstraction from iso-butane proved
to be quite difficult. The potential energy surface has many of the same
features as that of H-H-CCH, in particular, a small, early barrier that
leads to non-quadratic behaviour in the region of the saddle point. Owing
to the computational costs of these calculations, it was necessary to sacrifice
some accuracy in order to find the transition state. In the end, the values
of R1H = 1.2Å and R2H
= 1.5Å are in agreement with results
for abstraction from methane and benzene by the acetylene radical. The
large CI calculations strongly indicate that there is no barrier for
abstraction of hydrogen, the more conservative number giving a barrier
of only 0.45 kcal mol-1.
This again correlates with the large exothermicity
of this reaction, which is calculated from snap bond energies. If one considers
that the t-butyl group should relax somewhat at the CCCI transition state
and, thus, lower the energy of the barrier still, the argument for the
absence of a barrier becomes even more persuasive. Since this system is
a good model for the hydrogenated diamond (111) surface C-H bond, we conclude
that no barrier exists to abstraction of hydrogen from this surface by
acetylene. Barriers on other surfaces of diamond are probably non-existent
or negligibly small.

Now that it has been established that an alkynyl-tipped hydrogen abstraction
tool would be able to abstract hydrogen from diamond surfaces with little
or no thermodynamic hindrances, it would be desirable to find a method
for removing the hydrogen from the tip. A simple alternative, but less
elegant strategy is to make a new tip for each abstraction and dispose
of the tool after use. What makes the acetylene good at abstracting hydrogen
is the strength of its C-H bond. However, this bond is quite weak in the
3Bu excited state (see table 6).
We calculate a bond strength of 41.7 kcal mol-1
doing a GVBCI-SCF in which all 10 valence electrons are active in
10 orbitals, followed by a multi-reference
times singles and doubles configuration
interaction (MR*SD CI) in
which all configurations in the GVBCI with coefficients
< 0.05 are chosen as references. In the case of the triplet excited
state, there are four references and, in the case of dissociated H + CCH,
there are six references. The geometry for the excited state is optimized
at the MR*SD CI level. The molecule is not linear in this state, having
a C-C-H bond angle of 132.0°.
The C-C bond length also increases to 1.38 Å
from 1.20 Å for the ground state, reflecting the double bond
character of this bond. The weakening of the C-C bond in the excited state
leads directly to the weakening of the C-H bonds, as the triple bond character
can be restored upon dissociation of one of the C-H bonds. The weakening
of the C-H bond leaves the acetylene prone to abstraction, making it easy
to remove the hydrogen and refresh the tip. So photoexcitation of the alkynyl
tip from its ground state to the 1Bu
excited state, followed by relaxation
to the triplet would facilitate the breaking of the tip-hydrogen bond.
Drexler also made an alternative proposal for removing the hydrogen from
the tip [1].

5. Conclusion

We model the abstraction of hydrogen from
H2, CH4,
C2H2,
C6H6 and CH(CH3)3 by
the acetylene radical using accurate CI ab initio quantum-chemistry
techniques. From our results, conservative estimates show that the reaction
barriers for abstraction from sp3
hybridized carbons are negligible, or
zero for the case of isobutane. The barriers are small for sp2
hybridized carbons and slightly larger for sp hybridized carbons.
Therefore,
abstraction tools based on ethynyl radical molecular tips should reliably
and rapidly abstract hydrogen from most carbon
structures at moderate temperatures.
We also find that the hydrogen bond to the pi-pi* excited enthynyl tip
is relatively weak, and therefore can be broken to refresh the tip. We
have also shown how nanofabrication processes can be
accurately and inexpensively
designed in a computational framework.

Acknowledgments

We gratefully acknowledge the useful discussions with K Eric Drexler,
Siddharth Dasgupta and Erik P Bierwagen. CBM was supported by a Department
of Defense National Defense Science and Engineering Grant (NDSEG) fellowship
and JKP was partially supported by a BP America fellowship. This research
was partially supported by the Xerox Corporation. The facilities of the
Materials and Molecular Simulations Center were supported by grants
from NSF (NSF-CHE-9100284) and
ONR/NRL, and by grants from Allied-Signal, BP
America, Asahi Chemical, Asahi Glass, General Electric,
General Motors, Chevron and Xerox.